A single time-to-event, e.g., overall survival time, has been the typical primary endpoint in longitudinal cancer and HIV/AIDS studies. However, this outcome alone is generally inadequate to capture all the impacts, clinical and economic, that a treatment (and/or other covariates) might have. Comprehensive assessment of treatments has been increasingly advocated in recent years, and this effort has posed many unique statistical challenges. The broad objective of this research is to address some of these challenges in chronic disease research and develop new statistical methods. Major efforts will be directed toward (1) cost and cost-effectiveness analyses with incomplete follow-up data and (2) marginal analysis'^ time-between- events in multi-state processes and recurrent events. Current developments in these two areas are inadequate and substantial gaps of knowledge exist. Given that our health care system is increasingly constrained with limited resources, nowadays cost evaluation is becoming an important component in medical research and has been integrated in many studies. This work will focus on developing semiparametric estimation and regression procedures that accommodate right-censored data. The second area of research concerns the analysis of disease processes represented by multiple clinical states or recurrent events. Existing statistical methods largely target at time-to-events. This research will address time-between-events, which are of direct scientific interest in many circumstances. Despite the challenges of these long-standing problems, preliminary investigations have shown considerable promise for elegant and practical solutions. Large-sample properties of the proposed estimators will be rigorously investigated. Extensive simulation studies will be performed to validate these proposals under practical sample sizes. The proposed methods will be applied to a number of clinical studies. User-friendly computer programs will be developed and made available to the research community. [unreadable] [unreadable] [unreadable]